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Rational and complex numbers

    Date: 12 Jun 83 2346 EDT (Sunday)
    From: Guy.Steele at CMU-CS-A
    To:   Richard E. Zippel <RZ>
    cc:   common-lisp at SU-AI
    Re:   Rational and complex numbers

    I do foresee one entirely plausible application for Gaussian integers,
    which is graphics applications.  For discrete bit-map representations,
    Gaussian integers may be a very convenient representation.  Some interesting
    work has been done at Yale on picture languages that use complex numbers.

    I also admit once again to harboring the secret ambition for some form
    of LISP to supplant FORTRAN...
Another version of this would use an arbitrary two dimensional module
instead of the complex numbers.  For instance  I suspect that if you
associate the point (a, b) into a + sqrt(-163)*b, and then plot the powers
of (1+ sqrt(-163)) you will get some interesting results.  Similarly, taking
a some image and then multiplying it by a complex number can lead to
interesting versions of scaling.  Finally, the wrap around types of windows
we used in Space War might be best represented as GF(1031)[x]/(x^2+1) or
something (actually GF(1024)xGF(1024) would be more natural).